Triaxial weave for the production of stiff structural manifolds for use in structures and weaving method thereof

ABSTRACT

Woven structures must be made of materials that are sufficiently flexible that they can be woven together. This often results in a finished structure that is also flexible. Thus weaving has long been considered inadequate for the production of buildings and other objects requiring high levels of stiffness. The present invention relates to increasing the stiffness of triaxial-weave woven structural manifolds. The present invention provides for a new type of triaxial weave that allows for structural members of greater diameter and stiffness that are still flexible enough to accommodate the geometry of the weave. The result is structures having approximately eight times the structural stiffness of conventional triaxial-weave woven structures.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority to the earlier filed provisionalapplications having Ser. Nos. 62/406,045 and 62/511,992

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

MICROFICHE APPENDIX

Not applicable.

FIELD OF INVENTION

The present application claims priority to the earlier filed provisionalapplications having Ser. Nos. 62/406,045 and 62/511,992, and herebyincorporates the subject matter of the provisional applications in theirentirety.

The present invention relates to a pattern and geometry of weaving thatproduces manifolds with high bending stiffness and strength. A primaryapplication of the new type of weave is the structural framework ofbuildings.

BACKGROUND OF THE PRIOR ART

Woven objects are known to have high strength-to-weight ratios. This isbecause the structural material continues essentially unbrokenthroughout the woven object. Thus, the strength-to-weight ratio of thecompleted object approaches the strength-to-weight ratio of the materialit is constructed of. Objects that are not woven generally make use offasteners and adhesives to bind the components together into the largerobjects. The fasteners and adhesives add weight to the completed objectand structural material bonded together with fasteners and adhesives isgenerally less strong that the original structural material before it iscut.

While woven objects are known to have high strength, they are also knownto have low stiffness. In order to weave materials together, thematerials must be sufficiently flexible that they are able to be bentover and under each other into an interlocking woven pattern. Thus, theresulting woven manifold also has a high degree of flexibility.

While methods of weaving find difficulty in creating objects with sharpcorners because of the stiffness of the material woven, objects withrounded surfaces are created with ease. Wicker furniture is a goodexample. In contrast, objects made with fasteners and adhesives finddifficulty in creating smooth curves, but create straight-sidedangular-cornered objects with ease. Consider the logistics of building awooden staircase with screws as either a straight staircase or a spiralstaircase. For these reasons, the woven building concept has a uniquesynergy with the geodesic domes popularized by Buckminster Fuller. Mosteverything that makes a Fuller dome more difficult to build withconventional techniques, becomes an asset when the structure isre-envisioned as a woven building. While Fuller domes are structurallyefficient, they have been held back by the complexity of building andcovering them—too many cuts, odd shapes that create material waste, toomany fasteners, too many specialized fasteners and hubs. Joints andfasteners lead to snag points and expansion gaps that make covering andsealing the structure more difficult. The new woven dome takes all ofthe advantages of the Fuller domes and adds simple and low-costconstruction and covering.

Conventional triaxial-weave woven dome buildings use a 1-1 triaxialweave. This weave is shown in FIGS. 1, 2, and 3.

The structural material requires sufficient flexibility to be bent over,under, and around the other structural members or to be repetitivelyinserted through the appropriate openings in a partially completed wovenmanifold to create the geometry of the weave. This required flexibilitydegrades the overall stiffness of the entire structure. And even withextremely flexible building materials, like plastics, the largestallowable size of the structural members lead to a structure that haslow strength.

Contrary to all the advantages of weaving, including the reduced amountof measuring and cutting and the reduced need for fasteners andadhesives and the resulting high strength-to-weight ratio, weaving hasbeen found to be unsuitable for objects requiring high degrees ofstructural stiffness, like buildings. Thus, there is a need in the artfor a new type of weaving, that is compatible with stiffer less flexiblestructural materials that can produce structural manifolds with largedegrees of stiffness.

SUMMARY OF INVENTION

The application will use the following definitions:

“Woven members” are the linear structural elements that comprise thewoven object.

“Plainweave” is the most common type of weave in which the wovenstructural members pass intersecting members on alternate sides. Forexample, in the weaving of a building, if woven in “plainweave” thestructural member will pass one intersection on the interior of theintersecting woven member and will then pass the next intersection onthe exterior of the intersecting woven member. This pattern continuesalternating each intersection between interior and exterior.

“Basket weave” is a synonym for “plainweave”

“Wave number” defines the number of waves in the unit length and isinversely proportional to wavelength.

“Meander” is the alternating or approximately sinusoidal path taken by awoven member which allows it to pass over and under other woven membersin a defined pattern, locking the woven object together.

The present invention provides for a new type of weave, which is atriaxial 2-2 weave, that together with properly chosen woven members ofan appropriate material and thickness, can produce structural manifoldsof high stiffness, including double-curved manifolds that are suitablefor a greater variety of applications requiring high levels ofcompressive force and structural stiffness such as the structuralframework for a building.

The structural members of the preferred embodiment of the presentinvention pass alternately over two and under two other structuralmembers. With the same weave density and structural member thickness(diameter assuming structural members with a circular cross section),the maximum curvature required of the structural members isapproximately 35% of the value required in the corresponding 1-1 weave.One might initially think that the diameter of the structural memberscould be increased by a factor equal to the inverse of 0.35 (orapproximately 2.8) before the elastic limit of the material is reached.But a greater diameter requires a meander of greater amplitude to passover and under the larger intersecting members. The larger diametersimultaneously reduces the maximum curvature of the members. Thus, theallowed increase in diameter is not a factor of 2.8 but the square rootof the same. Bending stiffness increases with the fourth power ofdiameter, thus bending stiffness of the building's wall is increased bya factor of 8 by replacing the 1-1 weave with a 2-2 weave and takingfull advantage of the allowed increase in the diameter of the structuralmembers.

Strength is also increased by a factor equal to the increase incross-sectional area of the woven members or approximately 2.8. For mostdome structures, stability is a more significant structural issue thanstrength, and thus the factor 8 increase in wall stiffness, whichincreases the stability of short wavelength deformations, is of highvalue. Stiffness in tension and compression (resistance to lengthchange) is increased by a factor equal to the increase incross-sectional area of the structural members and for double curvedmanifolds, this increases structural stiffness for long wavelengthdeformations.

In attempting to make a woven building using the common 1-1 “plainweave” it quickly became apparent that the required stiffness (for theoverall strength of the building) and required flexibility (to allow thewoven members to bend over and under each other) were mutuallyexclusive. Biaxial weaves exhibit bias shift and are thereforeinappropriate for buildings for the lack of dimensional stability. Thus,the need in the art for a new type of weave that requires lessflexibility of the woven members and is thus suitable for buildingsrequiring higher levels of strength and stiffness was clear.

Weaving is a method of joining flexible linear structural elementstogether to form a two-dimensional or three-dimensional structure.Weaving generally accomplishes the joining by frustrating the desire ofthe linear structural elements to remain straight by forcing them tomeander over and under each other. The tendency of the structuralelements to be straight creates contact forces where they intersect withother structural members. These contact forces together with frictioncreates some traction between the structural members. This tractionaccumulated over the many intersections throughout the length of thestructural member substitutes for adhesives or fasteners and holds theentire structure together. The economic advantages of weaving stems fromits ability to use the linear structural members in full length, withoutcutting, the reduced need for fasteners and adhesives, and the abilityof the continuous length of structural material to transport forcesgreat distances through the object created.

Fabrics, textiles, and all woven objects can be characterized by thenumber of axial directions present in the woven pattern. The vastmajority of woven materials are biaxial. This means that there arefibers representing two axial directions. In conventional woven fabric,the fibers representing the two axial directions are called the “warp”and “weft” respectively. The warp is parallel to the original directionof manufacture on a loom but is otherwise equivalent to the weft. Thewarp and the weft are mutually perpendicular. Biaxial weaving is commonfor its simplicity. Two axial directions are the minimum number requiredto bind the woven members into a single object. Biaxial fabrics andtextiles demonstrate an instability in their dimensioning diagonal tothese two axial directions. These diagonal directions are often referredto as the “bias”. This dimensional instability in the bias direction canin some cases be advantageous. For in the production of clothing thereis often a need for the fabric to “stretch and move” with the subjectand these bias directions in the fabric can accommodate such changes indimension. To prevent these instabilities in the fabric, a minimum ofthree axial directions are needed, and triaxial fabric and textiles arethe simplest that meet this requirement. Buildings that shift and moveare undesirable, and thus woven buildings should use a triaxial weave.There are little or no fabrics produced with triaxial weaves for theextraordinary complexity of the machine that would be required toautomate their production.

The best-known method of constructing the woven building of the presentinvention is to weave the structural members together by hand. Thebuilding can initially be woven in a two-dimensional form, flat on theground, and then forced into a three-dimensional shape after thetopology of the weave is correct. For example, ropes and winches can beused to contract the circumference of a flattened building to bring itinto a three-dimensional shape.

The woven buildings can be secured to the ground by means of attaching afabric cover to ground anchors and tightening those attachments. Thistension force in the cover squeezes the building into the ground and theresulting friction holds the building in place.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 shows a perspective view of a woven building following the priorart 1-1 triaxial weave.

FIG. 2 shows the fundamental repeating unit of the prior art 1-1triaxial weave.

FIG. 3 shows a cross-sectional view of the prior art 1-1 triaxial weave.

FIG. 4 shows a perspective view of a woven building following thepresent invention 2-2 triaxial weave.

FIG. 5 shows the fundamental repeating unit of the present invention 2-2triaxial weave.

FIG. 6 shows a cross-sectional view of the present invention 2-2triaxial weave.

FIG. 7 shows a perspective view of a second example of a woven buildingfollowing the present invention 2-2 triaxial weave.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows an example woven building 101, comprised of woven members102, intersecting each other at intersections 103. The fundamentalrepeating element of the 1-1 triaxial weave (prior art) 106 is alsoshown. The weave is terminated by a bounding member 104.

FIG. 2 shows a detail of the 1-1 triaxial weave (prior art) withstructural elements woven members 202 and example intersections 203, andits fundamental repeating unit 206.

FIG. 3 shows a sectional view of the 1-1 triaxial weave (prior art) in across-sectional plane that is parallel and coincident with one of thewoven members and perpendicular to the surface of the woven manifold,with structural elements woven members 302 and example intersection 303also shown.

FIG. 4 shows an example woven building 401, comprised of woven members402, intersecting each other at intersections 403. The fundamentalrepeating element of the 2-2 triaxial weave (present invention) 407 isalso shown. The weave is terminated by a bounding member 404.

FIG. 5 shows a detail of the 2-2 triaxial weave (present invention) andits fundamental repeating unit 507. The smallest unit of the preferredembodiment of the weave of the present invention is shown in FIG. 5,with structural elements woven members 302 and example intersection 303also shown.

FIG. 6 shows a sectional view of the 2-2 triaxial weave (presentinvention) in a cross-sectional plane that is parallel and coincidentwith one of the woven members and perpendicular to the surface of thewoven manifold, with structural elements woven members 302 and exampleintersection 303 also shown.

FIG. 7 shows a woven building 701 having structural element wovenmembers 702 and example intersections 703 where structural elementsmeet. Door opening 705 formed separate of the bounding member 704.Fundamental repeating unit 707 is also shown.

A fastener can be used to bind the intersections together more tightlyto prevent the woven members from sliding against each other understructural load. Appropriate fasteners could be screws, cable ties, andrope or twine.

Woven dome buildings can be built “top down”, where the weave is startedat the center of the building (usually the building's highest point) andas the weave is continued outward the roof is lifted with a crane. Atsome point when the downward curve of the manifold causes the wovenmembers to be perpendicular or nearly so to the ground, they can be bentunder the structure and this will often cause the structure to begin tosupport itself, lifting the weight off the crane. This method involvesthe expense of a crane. Woven dome buildings can also be built “bottomup”, by beginning the weave at the ground and continuing it upward untilfinally closing the weave at the center point (usually the highestpoint). Because the walls of the building do not obtain their stabilityuntil the dome is complete, the walls are often too weak to climb on asa substitute for scaffolding during construction. Thus scaffolding isalso needed. The buildings can also be woven flat on the ground in aplanar arrangement. If this “flat weave” method is chosen, severalcircumferential woven members around the perimeter cannot be includingwhile still in the planar configuration due to the excessivecircumference. Once the weave is complete (except for thecircumferential members that cannot be added yet), the building can beerected. To erect the building, ropes are placed around thecircumference of the building and winched tight until the circumferenceof the planar weave lifts off the ground and the whole structure becomescurved upwards at its edges. As it is desired that the edges curvedownward instead of upward to lift the roof, the structure is theninverted. With the circumference ropes still in place, several ropes aretied to one edge of the structure and pulled across the structurecausing the whole structure to flip over like a pancake being cooked.Now the woven manifold has its edges curved downward and the centralarea of the manifold is held above the ground by the edges of themanifold. The winches are further tightened to reduce the circumferenceand lift the roof. As the circumference approaches its planned value,the final few circumferential woven members can be woven into thepattern. Weaving the building flat is the preferred method as it avoidsthe expense and danger of using a crane or scaffolding. If fastener areused to further secure the intersections, the fasteners in the upperportion of the building can be placed before the winches are completelytightened so that the intersections can be easily reached from theground without scaffolding.

The woven members can be made of any material that is sufficientlystrong and flexible. Polyvinyl chloride irrigation pipe is a good choicegiven these requirements. The fundamental repeating unit of the weave ofthe present invention can be placed on the pattern of (inside thetriangles of the pattern of) a geodesic dome of any class (class 1, 2,or 3) and any frequency or other patterns where the 5-edge vertexes areplaced possibly in a more irregular pattern, with or without a 5-edgevertex in the center of the structure. Negative solid curvature in themanifold (or building shape) can be accommodated by 7-edge vertexes. The5-edge vertexes are generally placed in areas of positive solidcurvature.

If the woven building is spherical or ellipsoidal, it can be truncatedat a level that leaves its widest point higher than its lowest point orground level. This provides headroom to the occupants of the buildingwhen they are standing near an interior wall.

Most raw material that can be used as woven members is acquired inlimited length and lengths must be joined together using a method thatis suitable for that material. For polyvinyl chloride irrigation pipe, asolvent cement and telescoping ends are common and suitable. The lengthsneed not be joined to achieve the required length at the beginning ofthe process. Simplicity can be found in weaving only one piece at a timeand joining them afterwards. In this way less length of material needsto be pulled through the weave and time and effort can be saved.Sometimes the material is sufficiently flexible that the pieces can bejoined to extend the length before being woven and then a loop of thematerial can be formed to store the extra length until the head of themember can be woven along the appropriate path far enough to consume theadded length.

The characteristic U-turn patterns that attach to the bounding member ordoor opening can be smoothly curved (as in the figures), bent in angularcorners, or the members can be terminated without a curve and the deadend of the terminated member can be fasted to the bounding member ordoor opening. The U-turns must also be fastened to the bounding memberor door opening in some way.

Some modes of structural deformation are facilitated by the wovenmembers sliding against each other, and the traction produced by theweave may be insufficient to prevent this sliding movement. Thus foradded structural stability, a fastener can be placed at eachintersection. Screws, cable ties, rope, and twine are suitablefasteners.

To weave in a new length and thus extend a woven member, the end of themember is taken through the appropriate openings in the existing weavebeing mindful to pass appropriately over and under in the requiredpattern of the present invention.

Unlike conventional geodesic domes, the buildings of the presentinvention are particularly suitable for textile covering because oftheir smooth snagless surface.

1. A building material used in construction comprising a 2-2 triaxialweave.
 2. The 2-2 triaxial weave of claim 1 comprised of woven memberswith a circular cross section.
 3. The 2-2 triaxial weave of claim 1where the intersections of the woven members are optionally secured witha fastener.
 4. A three-dimensional structural members comprising a 2-2triaxial weave.